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Make Your Own Gears 

Makej Projects 

Make Your Own Gears 

Written By: Dustyn Roberts 


One nice thing about gears is that if you know any two things about them - let's say outer 
diameter and number of teeth — you can use some simple equations to find everything else 
you need to know, including the correct center distance between them. In this project, we'll 
design and fabricate spur gears using free software (Inkscape) and an online store 
( that does custom laser cutting at affordable prices out of a variety of 
materials. If you have access to a laser cutter at a local school or hackerspace, even better! 
You can also print out the template and fix it to cardboard or wood to cut the gears by hand. 

This project is adapted from a blog post a student did in my first Mechanisms and Things 
That Move class at NYU's ITP. 

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Make Your Own Gears 

Step 1 — Make Your Own Gears 

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Make Your Own Gears 

• First, look over the anatomy of the 
spur gear pair in this figure and the 
vocab below. 

• Number of Teeth (N) 

• Pitch Diameter (D): The circle 
on which two gears effectively 
mesh, about halfway through the 
tooth. The pitch diameters of two 
gears will be tangent when the 
centers are spaced correctly. 

• Diametral Pitch (P): The number 
of teeth per inch of the 
circumference of the pitch 
diameter. Think of it as the 
density of teeth — the higher the 
number, the smaller and more 
closely spaced the teeth on a 
gear. Common diametral pitches 
for hobby-size projects are 24, 
32, and 48. The diametral pitch 
of all meshing gears must be the 

• Circular Pitch (p) = pi / P: The 
length of the arc between the 
center of one tooth and the 
center of a tooth next to it. This 
is just pi (n = 3.14) divided by 
the diametral pitch (P). Although 
rarely used to identify off-the- 
shelf gears, you may need this 
parameter when modeling gears 
in 2D and 3D software like we're 
doing here. As with diametral 
pitch, the circular pitch of all 
meshing gears must be the 

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Make Your Own Gears 


• Outside Diameter (D ): The 
biggest circle that touches the 
edges of the gear teeth. You can 
measure this using a caliper like's # TOL-00067. 
Note: Gears with an even 
number of teeth are easiest to 
measure, since each tooth has 
another tooth directly across the 
gear. On a gear with an odd 
number of teeth, if you draw a 
line from the center of one tooth 
straight through the center 
across the gear, the line will fall 
between two teeth. So, just be 
careful using outside diameter in 
your calculations if you 
estimated it from a gear with an 
odd number of teeth. 

• Center Distance (C): Half the 
pitch diameter of the first gear 
plus half the pitch diameter of 
the second gear will equal the 
correct center distance. This 
spacing is critical for creating 
smooth-running gears. 

• Pressure Angle: The angle 
between the line of action (how 
the contact point between gear 
teeth travels as they rotate) and 
the line tangent to the pitch 
circle. Standard pressure angles 
are, for some reason, 14.5° and 
20°. A pressure angle of 20° is 

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Make Your Own Gears 

better for small gears (and gears 
with few teeth), but it doesn't 
make much difference. It's not 
important to understand this 
parameter, just to know that the 
pressure angle of all meshing 
gears must be the same. 

Step 2 

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P = N/D 



["."„?, im c h(P) " 


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p°r*D!=lT*(D? a 

W = P*D 

™_ (CD) 

Pitch Diameter (D) 

CD = (Di + 3 )/2 

2Z b LV*Tm )& 

a, = MyJ e 

# All of these gear parameters relate 
to each other with simple 
equations. The equations in the 
table here come from the excellent 
(and free) design guide published 
by Boston Gear [PDF]. 

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Make Your Own Gears 

Step 3 

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• Download and install Inkscape from . It's a free, 
open-source vector-based drawing 
program similar to Adobe 
Illustrator. It plays well with most 
modern Windows, Mac, and Linux 
operating systems (check FAQ for 

• Goto 
sell/down... and download their 
Inkscape starter kit. This will give 
you a making guide (a PDF file) 
and three templates that relate to 
the sizes of materials Ponoko 
stocks. Unzip the file and save to 
somewhere you'll remember. 

• Open a new file in Inkscape. Under 
the File menu, go to Document 
Properties to get the window shown 
here. Change the default units in 
the upper right hand corner to 
inches. Back in the main window, 
change the rulers from pixels to 
inches in the toolbar. Your screen 
should look like this. Once set, exit 
that window. 

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Make Your Own Gears 

Step 4 

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Make Your Own Gears 

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) Make Projects 

• Now let's make some gears! Go to 
the toolbar and choose Extensions 
--> Render --> Gear. A small Gear 
window will pop up that gives you 
three options: Number of Teeth, 
Circular pitch, px, and Pressure 
angle. Leave Pressure angle alone 
— the 20° default is standard for 
off-the-shelf gears so it's a good 
place to start. In this figure you can 
see that I chose 28 teeth with a 
circular pitch of 24. Click Apply, 
then Close. 

• Note on circular pitch: In Inkscape, 
the circular pitch is given in pixels, 
not inches, as we're used to using 
in the equations in the above table. 
You can get different gear ratios by 
just choosing a circular pitch that 
looks good and varying the teeth 
number, but if you want to make 
gears that interface with off-the- 
shelf gears, you need to pay a little 
bit more attention. By default in 
Inkscape there are 90 pixels in 1 
inch. So if you set circular pitch to 
24px in the gear tool as done 
above, that rounds to 0.267 inches 
(24/90 = 0.2666...). 

• Since diametral pitch (P) = n I 
circular pitch (p), the diametral 
pitch (P) in inches is = n I 0.267 = 
1 1 .781 . You will not find any off- 
the-shelf gears with a diametral 
pitch of 1 1 .781 . As mentioned 
earlier, common diametral pitches 

Page 8 of 18 

Make Your Own Gears 

are 24, 32, and 48. So if you plan to 
make gears to play nice with off- 
the-shelf gears, start with the 
diametral pitch of your off-the-shelf 
gear and use the equations in the 
table to work backwards to what 
your circular pitch should be in 
pixels in Inkscape. 

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Make Your Own Gears 

Step 5 

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• Now, since one gear is no fun by 
itself, follow the last two steps 
again to make at least one more 
gear. The second gear shown in 
figure 30 has 14 teeth. Remember: 
The pressure angle and circular 
pitch must be the same for the 
gears to mesh - only change the 
number of teeth! 

• Use the circle tool and hold down 
the CTRL button (on a PC) to draw 
a circle inside the big gear. The 
default circle shows up filled in with 
black. Zoom in if you need to. 
Make sure the arrow selector is 
active and click on the circle. Make 
sure inches is selected in the 
toolbar and the lock button looks 
locked. Type 0.250 in the W box in 
the toolbar, press enter, and watch 
the H box change automatically. 
Your circle will resize to 0.250 
inches in diameter and your screen 
should look like this. 

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Make Your Own Gears 

Step 6 

• Click and drag a box around the big 
gear, small gear, and circle shape 
to select them all. From the menu 
bar, choose Object --> Fill and 
Stroke. A window that looks like 
this should pop up. 

• In the Fill tab, click the X button 
for no paint. 

• In the Stroke paint tab, click the 
button next to the X for flat color. 
Leave the color default (black) 
for now. 

• In the Stroke style tab, change 
the width to 0.030 mm and hit 
Enter. This is what Ponoko 
wants the line thickness to be 
for laser cuts. Adjust if 
necessary if you're using a 
different laser cutter. Close the 

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Make Your Own Gears 

Step 7 

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• Now we need to get this circle in 
the exact center of the gear. Make 
sure the arrow selector is active. 
Click and drag a box around the big 
gear and the circle to select them 
both. On the menu bar, go to 
Object --> Align and Distribute. 
Click on the "center object 
horizontally" button highlighted 
here, then the one right below it - 
"center objects vertically." Now you 
have a gear with a hole perfectly 
centered! Copy and paste this 
circle and repeat this step to center 
a circle in the other gear. 

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Make Your Own Gears 

Step 8 

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Make Your Own Gears 

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) Make Projects 

• Now that we have our gears, let's 
create a base with holes spaced 
the correct distance apart so we 
can mount the gears with 1/4" 
wooden dowels and make them 

• First, we need to calculate what 
the center distance (CD) of our 
gears is using the equations 
from the table. Both of our gears 
have a circular pitch of 24 px 
and a pressure angle of 20°. 
The big gear has 28 teeth and 
the small one has 14. In the note 
on step 4, we converted the 
circular pitch in pixels to a 
diametral pitch in inches of 
11.781. If we look at the table, 
all we need is that number and 
the numbers of teeth on the two 
meshing gears to find the center 
distance (CD). Use the equation 
CD = (N1 + N2)/2P and you'll 
find that CD = 1.783. 

• Now, copy one of the circles 
inside the gears, and paste two 
of them about two inches apart 
on the lower part of the template. 
Select the one farthest to the 
left, and change the X coordinate 
in the toolbar to 3 inches, then 
hit Enter. Your screen should 
look like this. 

• Use the same procedure to 
place the second circle to the 
right of the first with an X 

Page 14 of 18 

Make Your Own Gears 

coordinate of 4.783. This is the 
center distance we calculated 
above (1 .783) added to the X 
coordinate of the first circle 

Step 9 

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• Now draw a rectangle around the 
two circles to complete the base. 
Align the rectangle with the two 
circles as shown here. 

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Make Your Own Gears 

Step 10 

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• Now we need to prepare the file to 
be uploaded and ordered on 

• Ponoko uses colors to indicate 
how they should treat the files — 
for example, a blue 0.030 mm 
line means cut it all the way 
through. So select everything 
you've drawn so far, go to the 
color swatches at the bottom of 
the screen, and hold down the 
shift button while you click on 

• Open the P1 .svg template you 
downloaded earlier. Select 
everything you have drawn so 
far, and copy and paste it into 
this template as shown here. 
Don't worry about the orange 
border and words — Ponoko 
knows only to cut the blue 

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Make Your Own Gears 

Step 11 

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• Save the file and go to 
to set up a free account, upload it, 
pick a material, and get it shipped! 
I chose blonde bamboo as shown 
here and the total cost was just 
$4.13 (plus shipping). 

• Note: Once you open your free 
account, go to My Accounts --> 
Preferences to set your 
shipping hub to "Ponoko - United 
States" (or the closest location 
to you). Mine was accidentally 
set to New Zealand so my 
shipping charges were curiously 
high until I figured this out. 

• Your Ponoko order should arrive 
in a couple of weeks, unless you 
specify a rush. While you're 
waiting, get a 1/4" wooden dowel 
from your local hardware or craft 
store (or McMaster-Carr, of 
course). Cut off two 2" sections 
with a hobby knife and file down 
any splintery ends. 

• The gears will come in the 
square template with a sticky 
paper protector on each side. 
Peel off the paper, pop out the 
gears, and position the two 
gears over the holes in the base. 
Insert your wooden dowels, and 

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Make Your Own Gears 

This project is an excerpt from my upcoming book, Making Things Move . 

This document was last generated on 2012-10-31 01:23:06 AM. 

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